Question

$\large\red{\sf{Question \: \: 1}}$
If the sum of the lengths of bases of a trapezium is 12 cm and area is 14.1 cm² then it's altitude will be:
$\large\red{\sf{Question \: \: 2}}$
If the length, width and height of a cuboid tare 4.2 m, 3 m and 1.1 m, then its capacity in litres will be:
$\large\red{\sf{Question \: \: 3}}$
A road roller is 350 cm long and its diameter is 84 cm. It takes 500 complete revolutions to travel the road. The area covered by it in m² will be:
$\large\red{\sf{Question \: \: 4}}$
A solid cuboidal piece of wood measures 3 m x 2.5 m x 8 cm. Find the weight of the piece if 1 cubic cm of wood weighs 9 grams?
$\large\red{\sf{Question \: \: 5}}$
A well was dug with 14 m inner diameter and was 8 m deep. The earth dug out of it was evenly spread out on a rectangular plot of size 10 m x 8 m. Find the raise in the height of the plot?​

Answer 1

Solution :-

1)

Given that

The sum of the lengths of bases of a trapezium

(a+b) = 12 cm

Let the altitude of the trapezium be h cm

We know that

Area of a trapezium = (1/2)h(a+b) sq.units

According to the given problem

Area of the trapezium = 14.1 cm²

=> (1/2)×h×12 = 14.1

=> 12h/2 = 14.1

=> 6h = 14.1

=> h = 14.1/6

=> h = 2.35 cm

The altitude of the trapezium = 2.35 cm

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2)

Given that

Length of a cuboid (l) = 4.2 m

Breadth of the cuboid (b) = 3 m

Height of the cuboid (h) = 1.1 m

We know that

Volume of a cuboid = lbh cubic units

Volume of the cuboid = 4.2×3×1.1 m³

=> Volume of the cuboid = 13.86 m³

The capacity of the cuboid = 13.85 m³

We know that

1 m³ = 1000 litres

13.85 m³ = 13.85×1000 l = 13850 litres

The capacity of the cuboid is 13,850 litres

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3)

Given that

The diameter of the road roller

(d) = 84 cm

The radius of the roller = Diameter/2

=> r = 84/2

=> r = 42 cm

Radius of the roller = 42 cm

The length of the roller = 350 cm

=> The height of the roller = 350 cm

The Area covered by the roller in one revolution

= Curved Surface Area of the cuboid

= 2πrh sq.units

=2 ×(22/7)×42×350 cm²

= 2×22×6×350 cm²

= 92400 cm²

The number of revolutions completed by the roller = 500

The complete area covered by the roller

= 92400×500 cm²

= 46200000 cm²

We know that

1 m² = 10000 cm²

=> 46200000 cm² = 46200000/10000

= 4620 m²

The Area covered by the roller is

4620 m²

----------------------------------------------------

4)

Given that

The dimensions of the cuboid

= 3 m x 2.5 m x 8 cm.

We know that

1 m = 100 cm

The dimensions are 300 cm × 250 cm × 8 cm

We know that

Volume of a cuboid = lbh cubic units

Volume of the cuboid

= 300×250×8 cm³

= 600000 cm³

Volume of the cuboid = 600000 cm³

The weight of the piece of 1 cubic cm of wood = 9 grams

The total weight of the wood of 600000 cm³

= 600000×9 grams

= 5400000 grams

= 5400000/1000 kg

= 5400 kg

Total weight is 5400 kg

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5)

Given that

The inner diameter of the well (d) = 14 m

Radius = Diameter/2 = 14 /2 = 7 m

Depth of the well (h) = 8 m

The well is in the shape of a cylinder

Volume of a cylinder = πr²h cubic units

=> (22/7)×7²×8 m³

=> Volume = 22×7×8 m³

=> Volume = 1232 m³

The dimensions of the rectangular plot

= 10 m and 8 m

Let the height of the plot be h m

Volume of the rectangular plot

= Volume of the cuboid

= lbh cubic units

= 10×8×h m³

= 80 h m³

Volume of the rectangular plot = 80h m³

According to the given problem

Volume of the rectangular plot = Volume of the sand dug out of the well

=> 80h = 1232

=> h = 1232/8

=> h = 154 m

The raise in the height of the plot is

154 m

Answer 2

Answer:

1)

Given that

the sum of length of base of the trapezium

(a+b) = 12

we know that area of trapezium is

1/2h(a+b)

according to the problem

area of trapezium is 14.1cm^2

1/2*h*12

12h/2=14.1

6h=14.1

h=2.35

2)

Given that

length of cuboid = 4.2m

height of cuboid = 1.1m

width of cuboid = 3m

we know that volume of cuboid is

LBH cubic units

Volume of cuboid =4.2*1.1*3

=> Volume of cuboid is 13.86

we know that

1m^3=1000liters

13.86m^3= 13.86*1000

capacity of cuboid is 13860 liters